The Rhode Island National Guard has started going door to door in coastal areas to inform any New Yorkers who may have come to the state that they must self-quarantine for 14 days.
Rhode Island Governor Gina Raimondo expanded the mandatory self-quarantine to anyone visiting the state.
The move comes as residents of states with a large number of out-of-town visitors and holiday homeowners fear those escaping major cities being hit by the virus would inadvertently bring it with them.
Ms Raimondo also ordered residents to stay at home, unless they needed to buy food, medicine or go to the doctor.
She ordered non-essential retail businesses to close from Monday until April 13 to help stop the spread of the virus.
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She also directed property agents and hotel operators to include requirements in new purchase agreements for any out-of-state residents to quarantine for 14 days.
On Friday, state police set up a motorway checkpoint in Hope Valley, near the border with Connecticut, where drivers with New York licence plates must stop and provide contact information.
Police also told New York motorists to self-quarantine for two weeks, local media reported.
If New Yorkers don’t comply, they face fines and jail, Ms Raimondo said.
“I want to be crystal clear about this: if you’re coming to Rhode Island from New York you are ordered into quarantine," she said.
"The reason for that is because more than half of the cases of coronavirus in America are in New York.”
Ms Raimondo said the order was not meant to be discriminatory.
New York Governor Andrew Cuomo called the order “reactionary” and unconstitutional, saying he would sue Rhode Island if the policy wasn’t rescinded.
He said he believed the states could “work it out".
“I understand the goal … but there’s a point of absurdity and I think what Rhode Island did is at that point of absurdity,” Mr Cuomo said.
“We have to keep the ideas and the policies we implement positive rather than reactionary and emotional.”
On Saturday, US President Donald Trump said he had spoken with some governors and was considering some type of quarantine to prevent people in New York and parts of New Jersey and Connecticut from travelling out of their states.
But Mr Trump later tweeted that a travel advisory should be administered and not a quarantine.
He said it would be for a “short period of time, if we do it at all".
Last Thursday, Texas Governor Greg Abbott joined officials of other states in imposing quarantines on people travelling from the New York area by air, as well as passengers from New Jersey, Connecticut and New Orleans – places where Covid-19 outbreak is more severe.
Mr Abbott said travellers who didn’t comply with the 14-day quarantine risked jail. State troopers would conduct visits to make sure people were staying put, he said.
In Rhode Island, which reported its first two deaths from Covid-19 on Saturday, a police officer and a member of the National Guard visited stately and modest coastal homes in the Westerly neighbourhood of Watch Hill to collect contact information from New Yorkers and tell them to self-quarantine.
The officers expected to go to about 1,000 homes over a few days.
“This is more of an education tool to make people aware and comply with what we are asking them to do,” Westerly police chief Shawn Lacey said.
“We are certainly hoping it doesn’t get to enforcement action that has to happen.”
Reha Kocatas, a New Yorker who travelled to his Rhode Island home from the Bahamas on March 22, said his wife and two children were visited by a police officer and a member of the National Guard.
Already under a state-ordered 14-day quarantine because he travelled from abroad, Mr Kocatas said he volunteered information to the authorities, including the number of people in the home, when they entered Rhode Island and his and his wife’s date of birth.
But he questioned why it was necessary to send a police officer to his door.
“It seemed like a pretty large waste of resources for something that could have been volunteered through an online form pretty quickly,” he said.
“If New Yorkers are such high-risk individuals, why are we putting first responders in front of these individuals is a little questionable since there is no action item at the end of the day.
“They weren’t going to remove us. It seemed like bureaucratic grandstanding.
"The local community that happens to be here believes that it’s a waste of precious resources when time is of the essence in preparing for other things.”
Ms Ramaindo said only an estimated 50 per cent of Rhode Island residents were complying with social distancing measures, with crowds spotted at a beach, groups at parks, as well as crowds at shops and house parties.
As a result, she banned gatherings of more than five people and urged people to limit interactions to the that number.
“I’ve said it last week, I’m going to say it again, knock it off. You are risking the lives of everyone in this state,” she said.
People able to work from home must do so, she said.
Residents who work in Massachusetts and must travel to that state must self-quarantine at home when they return, she said.
For most people, the virus causes mild or moderate symptoms, such as fever and cough that clear up in two to three weeks.
For some, especially older adults and people with existing health problems, it can cause more severe illness, including pneumonia, and can also be deadly.